Multiplicativity conjecture for commutativity degrees of coprime direct products

Let $H$ and $K$ be finite groups of coprime orders, and let $\mathcal{D}(X)$ denote the set of commutativity degrees of a finite group $X$.

Multiplicativity conjecture. For any two such groups,

$$|\mathcal{D}(H\times K)|=|\mathcal{D}(H)|\times|\mathcal{D}(K)|.$$

The product formula for the sets themselves gives the immediate lower bound $|\mathcal{D}(H\times K)|\geqslant|\mathcal{D}(H)|+|\mathcal{D}(K)|$. The stated conjecture predicts the stronger exact product formula for their cardinalities and is presented as unresolved in the source.